Asymptotic Expansion of the Modified Exponential Integral Involving the Mittag-Leffler Function

Richard Paris
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Richard Paris: Division of Computing and Mathematics, Abertay University, Dundee DD1 1HG, UK

Mathematics, 2020, vol. 8, issue 3, 1-13

Abstract: We consider the asymptotic expansion of the generalised exponential integral involving the Mittag-Leffler function introduced recently by Mainardi and Masina [ Fract. Calc. Appl. Anal. 21 (2018) 1156–1169]. We extend the definition of this function using the two-parameter Mittag-Leffler function. The expansions of the similarly extended sine and cosine integrals are also discussed. Numerical examples are presented to illustrate the accuracy of each type of expansion obtained.

Keywords: asymptotic expansions; exponential integral; Mittag-Leffler function; sine and cosine integrals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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